Corrugated silicon metasurface optimized within the Rayleigh hypothesis for anomalous refraction at large angles

We optimize optical performance of metasurfaces based on periodically corrugated silicon layers by adjusting the Fourier coefficients of their surface profile. For smooth corrugations, we demonstrate an excellent quantitative accuracy of semi-analytical approach based on the Rayleigh hypothesis. We employ the approach to design metasurfaces with anomalous refraction due to dominant first order diffraction. Unlike conventional Huygens' dielectric metasurfaces, corrugated silicon layers are capable of efficient anomalous refraction in grazing directions: we obtain corrugation shapes allowing to deflect 70-80% of the energy of normally incident green light into the range of 68{\deg}-85{\deg} of angles with respect to the normal.